Foundations of Materials Science and Engineering
Foundations of Materials Science and Engineering
6th Edition
ISBN: 9781259696558
Author: SMITH
Publisher: MCG
bartleby

Concept explainers

bartleby

Videos

Question
Book Icon
Chapter 12.15, Problem 85AAP
To determine

The tensile modulus of the composite in the direction of the fibers.

The elastic strain in the composite.

Expert Solution & Answer
Check Mark

Answer to Problem 85AAP

The tensile modulus of the composite in the direction of the fibers is 347GPa.

The elastic strain in the composite is 4.19×103.

Explanation of Solution

Write the equation for the rule of mixture for the ceramic-matrix composites.

  Ecomp=fAl2O3EAl2O3+fSiCESiC                                                                                   (I)

Here, modulus of elasticity of composite is Ecomp, modulus of elasticity of silicon carbide fiber is ESiC, volume fraction of silicon carbide fiber is fSiC, modulus of elasticity of aluminum oxide matrix is EAl2O3 and volume fraction of aluminum oxide matrix is fAl2O3.

Write the equation to calculate the elastic strain in the composite.

  εcomp=σcompEcomp=(Pcomp/Acomp)Ecomp                                                                                              (II)

Here, elastic strain in the composite is εcomp, tensile strength of composite is σcomp, load applied on the composite is Pcomp and surface area of the composite is Acomp.

Conclusion:

Substitute 340GPa for ESiC, 350GPa for EAl2O3, 0.70 for fAl2O3 and 0.30 for fSiC in Equation (I).

 Ecomp=(0.70)(350GPa)+(0.30)(340GPa)=347GPa

Thus, the tensile modulus of the composite in the direction of the fibers is 347GPa.

Substitute 8MN for Pcomp, 55cm2 for Acomp and 347GPa for Ecomp in Equation (II).

 εcomp=(8MN/55cm2)347GPa=(8MN55cm2×1m210000cm2)347×103MPa=4.19×103

Thus, the elastic strain in the composite is 4.19×103.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
Continuity equation A y x dx D T معادلة الاستمرارية Ly X Q/Prove that ди хе + ♥+ ㅇ? he me ze ོ༞“༠ ?
Q Derive (continuity equation)? I want to derive clear mathematics.
motor supplies 200 kW at 6 Hz to flange A of the shaft shown in Figure. Gear B transfers 125 W of power to operating machinery in the factory, and the remaining power in the shaft is mansferred by gear D. Shafts (1) and (2) are solid aluminum (G = 28 GPa) shafts that have the same diameter and an allowable shear stress of t= 40 MPa. Shaft (3) is a solid steel (G = 80 GPa) shaft with an allowable shear stress of t = 55 MPa. Determine: a) the minimum permissible diameter for aluminum shafts (1) and (2) b) the minimum permissible diameter for steel shaft (3). c) the rotation angle of gear D with respect to flange A if the shafts have the minimum permissible diameters as determined in (a) and (b).

Chapter 12 Solutions

Foundations of Materials Science and Engineering

Ch. 12.15 - Prob. 11KCPCh. 12.15 - Prob. 12KCPCh. 12.15 - Prob. 13KCPCh. 12.15 - Prob. 14KCPCh. 12.15 - Prob. 15KCPCh. 12.15 - Describe the sheet-molding compound manufacturing...Ch. 12.15 - Prob. 17KCPCh. 12.15 - Prob. 18KCPCh. 12.15 - What are the basic raw materials for portland...Ch. 12.15 - What are the names, chemical formulas, and...Ch. 12.15 - List the five main ASTM types of portland cement...Ch. 12.15 - What is asphalt? Where is asphalt obtained?Ch. 12.15 - What are chemical composition ranges for asphalts?Ch. 12.15 - What does an asphalt mix consist of? What is the...Ch. 12.15 - Prob. 25KCPCh. 12.15 - What are the subrings of the annual growth rings...Ch. 12.15 - Prob. 27KCPCh. 12.15 - Prob. 28KCPCh. 12.15 - Prob. 29KCPCh. 12.15 - Prob. 30KCPCh. 12.15 - Prob. 31KCPCh. 12.15 - Prob. 32AAPCh. 12.15 - Prob. 33AAPCh. 12.15 - Prob. 34AAPCh. 12.15 - Prob. 35AAPCh. 12.15 - Prob. 36AAPCh. 12.15 - Prob. 37AAPCh. 12.15 - Prob. 38AAPCh. 12.15 - Prob. 39AAPCh. 12.15 - A unidirectional carbon fiberepoxy resin composite...Ch. 12.15 - Prob. 41AAPCh. 12.15 - Prob. 42AAPCh. 12.15 - Prob. 43AAPCh. 12.15 - Prob. 44AAPCh. 12.15 - Prob. 45AAPCh. 12.15 - If the tensile strength of the Kevlar 49 fibers is...Ch. 12.15 - Prob. 47AAPCh. 12.15 - Prob. 48AAPCh. 12.15 - Prob. 49AAPCh. 12.15 - Prob. 50AAPCh. 12.15 - Prob. 51AAPCh. 12.15 - What types of chemical reactions occur during the...Ch. 12.15 - Prob. 53AAPCh. 12.15 - Which component of portland cement hardens rapidly...Ch. 12.15 - Prob. 55AAPCh. 12.15 - Prob. 56AAPCh. 12.15 - Prob. 57AAPCh. 12.15 - Prob. 58AAPCh. 12.15 - Prob. 59AAPCh. 12.15 - Prob. 60AAPCh. 12.15 - Prob. 61AAPCh. 12.15 - Prob. 62AAPCh. 12.15 - Prob. 63AAPCh. 12.15 - Prob. 64AAPCh. 12.15 - Prob. 65AAPCh. 12.15 - Prob. 66AAPCh. 12.15 - Prob. 67AAPCh. 12.15 - Prob. 68AAPCh. 12.15 - Prob. 69AAPCh. 12.15 - What characteristics are desirable for the...Ch. 12.15 - Prob. 71AAPCh. 12.15 - Prob. 72AAPCh. 12.15 - Prob. 73AAPCh. 12.15 - Prob. 74AAPCh. 12.15 - Prob. 75AAPCh. 12.15 - Prob. 76AAPCh. 12.15 - Prob. 77AAPCh. 12.15 - Why does wood shrink much more in the transverse...Ch. 12.15 - A newly developed metal-matrix composite is made...Ch. 12.15 - Prob. 81AAPCh. 12.15 - Prob. 82AAPCh. 12.15 - Prob. 83AAPCh. 12.15 - Prob. 84AAPCh. 12.15 - Prob. 85AAPCh. 12.15 - Prob. 86AAPCh. 12.15 - Prob. 87SEPCh. 12.15 - Prob. 88SEPCh. 12.15 - Prob. 89SEPCh. 12.15 - Prob. 90SEPCh. 12.15 - Prob. 91SEPCh. 12.15 - Prob. 92SEPCh. 12.15 - (a) In Problem 12.94, if all three beams are to...Ch. 12.15 - Prob. 97SEPCh. 12.15 - Prob. 98SEPCh. 12.15 - Prob. 99SEPCh. 12.15 - Prob. 100SEPCh. 12.15 - Prob. 101SEPCh. 12.15 - Prob. 102SEPCh. 12.15 - Prob. 103SEPCh. 12.15 - Prob. 104SEPCh. 12.15 - In total hip replacement, most surgeons prefer a...
Knowledge Booster
Background pattern image
Mechanical Engineering
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Elements Of Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press
Text book image
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON
Text book image
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education
Text book image
Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY
Text book image
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Text book image
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY
composite-materials; Author: Tonya Coffey;https://www.youtube.com/watch?v=Vu6ik-bcKf4;License: Standard youtube license